Alrighty, well first off let me state I'm still learning and I apologize if this is absolutely confusing, or totally wrong. But, my brother owns a Sony 75-300mm lens, and I was reading a few things about DOF. So, setting the lens at 75mm, with an F number of 4.5, will generate the greatest depth of field yes? And I also read if I were to back up, and zoom in further, I could deepen the depth of field even MORE? How's that possible? Sorry if that's confusing, or just not right at all. Thanks!

Don't worry about asking questions: that's a lot of what the CameraLabs forum is about, though we always prefer members to try and find answers for themselves first as that saves other member's time and is, in any event, a better way to learn.

Equivalent focal lengths - Most of us greybeards were brought up with 35mm film cameras and in those days everyone knew what to expect in terms of field of view from lenses of different focal lengths. But with digital sensors that all changed as the sensors are more often than not not only smaller than a frame of 35mm film but are of different sizes. So, for example, if you took a 50mm focal length lens, good for general shots on a 35mm film camera, and stuck it in front of of your SX1 IS sensor the picture would be heavily cropped because your sensor is a lot smaller than the film. So, from the Canon USA SX1 IS Specifications page, while the actual focal length of your camera's lens varies from 5.0 to 100.0mm it gives the equivalent field of view on a piece of 35mm film equivalent to focal lengths varying from 28mm to 560mm.

Depth of Field - I can do no better than refer you to the CambridgeInColour Understanding Depth of Field tutorial. Understanding why DoF works the way it does can be difficult to get your head around but if you don't want to get into the theory then just have a play with the DoF calculator which is part of the tutorial and try to get a feel for how the numbers pan out on the camera(s) of your choice.

Deepening the depth of field (DOF) means to put more 'ranges of distances from the camera' into focus.

Telephoto lenses have shallower DOF than wide-angle lenses, when comparing between image sensors of the same size. (Image sensors are the digital 'film'). Therefore, using the same lens settings on any two brands of lenses will technically give the same DOF. The lens brand doesn't actually matter; its focal length and aperture settings do.

Zooming in further with any lens (which is increasing the focal length) will give a shallower DOF, which means anything distant from what you're focusing on will be out-of-focus (OOF).

Telephoto lenses are often used for their stronger OOF effects. Such OOF parts of the image are known as 'bokeh'. See http://en.wikipedia.org/wiki/Bokeh for more useful information on this.

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'Equivalency' refers to the conversion of focal lengths to make them the same focal length as on 35mm film size, or whatever is being used as the gauge, because many photographers are used to this film size.
Even when using the same focal length, lenses have different angles of view because of different image sensor sizes.

What do I mean?

Well, it's difficult to explain without confusing you any further, so please visit this very useful website for much more useful information - http://www.cambridgeincolor.comMay I bring your attention to the 'Camera lenses: Understanding focal length and aperture' and 'Understanding depth of field' articles.